Solve these equations.?

Question

1) 3ln2x-1=14

2) 6^2x+1=11

3) log(2x-3)=2

Answer 1

1) 3ln2x-1=14
3ln2x = 15
ln2x = 5
2x = e^5
x = (e^5)/2
x = 74.2

2) 6^(2x+1)=11
lg6^(2x+1) = lg11
(2x+1)lg6 = lg11
2x+1 = lg11/lg6
x = [(lg11/lg6) - 1]/2
x = 0.169

3) log(2x-3)=2
2x-3 = 10^2
2x-3 = 100
2x = 103
x = 51.5

Answer 2

1. 3ln2x - 1 = 14 add one to both sides
3ln2x = 15 divide three by both sides
ln 2x = 5 to get rid of ln raise e^ to both
sides
e^ln2x = e^5 I don't have a calculator, but e^ln
cancels out
2x = e^5 divide two by both sides
x = e^5/2

2. 6^2x + 1 = 11 subtract one from both sides
6^2x = 10 take to the log of both sides
log 6 ^2x = log 10 power property
2x(log 6) = log 10 divide log 6 by both sides
2x = log 10/log6 use calculator then divide by 2

3. use the definition and change it to exponential form:
10^2 = 2x - 3
100 = 2x - 3 add three to both sides
103 = 2x divide by 2
103/2 = x

Answer 3

Question 1
3 ln (2x) = 15
ln(2x) = 5
2x = e^5
x = e^5 / 2
x = 74.2
Question 2
logs to base ten:-
2x.log 6 = log 10
x = 1 / 2.log 6
x = 0.643
Question 3
log(2x - 3) = 2
2x - 3 = 10²
2x - 3 = 100
2x = 103
x = 51.5

Answer 4

1) 3ln2x-1=14 add 1 to each side
3 ln 2x=15 divide both sides by 3
ln 2x=5 exponentiate both sides
2x=e^5 divide both sides by 2
x=½e^5
x=74.2

2) 6^2x+1=11 subtract 1 from each side
6^2x=10 take log of both sides
2x log 6=1 divide both sides by 2 log 6
x=1/(2 log 6)
x=0.6425

3) log(2x-3)=2 take 10^ both sides
2x-3=10²=100 add 3 to each sides
2x=103 divide both sides by 2
x=51.5

Answer 5

1)
3ln2x -1=14
3ln2x=15
ln2x=5
2x=e^5 e=2.7183
x=2(2.7183^5)
x=74.2066

2)
6^2x+1=11
log 6^2x =log(11-1)
2x log 6 = log 10
2x =log 10/log6
x= .389

3)
2x-3 =10^2
2x = 103
x= 51.5